Besides the two tasks described above, we attempt to enforce rotation invariance for the network. Inspired by [1]} and [2]}, we introduce self-supervised learning to our model. Self-supervision is helpful to capture general features without labels.
Specifically, we rotate the base set to 4 degrees, i.e., \(\lbrace 0^{\circ }, 90^{\circ }, 180^{\circ }, 270^{\circ } \rbrace \) , then use the softmax activation function to predict the image rotations. We map the base data (after rotation) to rotation-based label space, e.g., \(\mathbf {x} \rightarrow \mathbf {z}^{ss}\) , where \(\mathbf {z}^{ss} = [z^{ss}_1,z^{ss}_2,z^{ss}_3,z^{ss}_4] \in \mathbb {R}^{4}\) , then employ Equation REF  to achieve the rotation-based probability distribution \(\mathbf {y}^{ss}=[y^{ss}_1,y^{ss}_2,y^{ss}_3,y^{ss}_4] \in \mathbb {R}^{4}\) . Next, introduce categorical cross entropy function \(\mathcal {F}_{cce}\)  to compute the self-supervised auxiliary loss \(\mathcal {L}^{ss}\)  by:
\(\begin{split}\mathcal {L}^{ss} (x,\hat{\mathbf {y}}^{ss})&=-\sum _{c=1}^{4} \hat{y}^{ss}_c log(y^{ss}_c)\end{split}\) 
